Problem Transformed CSR 04 Ex2 Luc03b L

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex2 Luc03b L

stdout:

YES(?,O(n^1))

Problem:
fst(0(),Z) -> nil()
fst(s(),cons(Y)) -> cons(Y)
from(X) -> cons(X)
add(0(),X) -> X
add(s(),Y) -> s()
len(nil()) -> 0()
len(cons(X)) -> s()

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {8,7,6,5}
   transitions:
    s1() -> 8,7
    01() -> 8*
    cons1(2) -> 6,5
    cons1(4) -> 6,5
    cons1(1) -> 6,5
    cons1(3) -> 6,5
    nil1() -> 5*
    fst0(3,1) -> 5*
    fst0(3,3) -> 5*
    fst0(4,2) -> 5*
    fst0(4,4) -> 5*
    fst0(1,2) -> 5*
    fst0(1,4) -> 5*
    fst0(2,1) -> 5*
    fst0(2,3) -> 5*
    fst0(3,2) -> 5*
    fst0(3,4) -> 5*
    fst0(4,1) -> 5*
    fst0(4,3) -> 5*
    fst0(1,1) -> 5*
    fst0(1,3) -> 5*
    fst0(2,2) -> 5*
    fst0(2,4) -> 5*
    00() -> 1*
    nil0() -> 2*
    s0() -> 3*
    cons0(2) -> 4*
    cons0(4) -> 4*
    cons0(1) -> 4*
    cons0(3) -> 4*
    from0(2) -> 6*
    from0(4) -> 6*
    from0(1) -> 6*
    from0(3) -> 6*
    add0(3,1) -> 7*
    add0(3,3) -> 7*
    add0(4,2) -> 7*
    add0(4,4) -> 7*
    add0(1,2) -> 7*
    add0(1,4) -> 7*
    add0(2,1) -> 7*
    add0(2,3) -> 7*
    add0(3,2) -> 7*
    add0(3,4) -> 7*
    add0(4,1) -> 7*
    add0(4,3) -> 7*
    add0(1,1) -> 7*
    add0(1,3) -> 7*
    add0(2,2) -> 7*
    add0(2,4) -> 7*
    len0(2) -> 8*
    len0(4) -> 8*
    len0(1) -> 8*
    len0(3) -> 8*
    1 -> 7*
    2 -> 7*
    3 -> 7*
    4 -> 7*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(1))
Input	Transformed CSR 04 Ex2 Luc03b L

stdout:

YES(?,O(1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex2 Luc03b L

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  fst(0(), Z) -> nil()
     , fst(s(), cons(Y)) -> cons(Y)
     , from(X) -> cons(X)
     , add(0(), X) -> X
     , add(s(), Y) -> s()
     , len(nil()) -> 0()
     , len(cons(X)) -> s()}

Proof Output:
  'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:

  Details:
  --------
    'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
     'Bounds with minimal-enrichment and initial automaton 'match''
     --------------------------------------------------------------
     Answer:           YES(?,O(n^1))
     Input Problem:    innermost runtime-complexity with respect to
       Rules:
         {  fst(0(), Z) -> nil()
          , fst(s(), cons(Y)) -> cons(Y)
          , from(X) -> cons(X)
          , add(0(), X) -> X
          , add(s(), Y) -> s()
          , len(nil()) -> 0()
          , len(cons(X)) -> s()}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  fst_0(2, 2) -> 1
        , 0_0() -> 1
        , 0_0() -> 2
        , 0_1() -> 1
        , nil_0() -> 1
        , nil_0() -> 2
        , nil_1() -> 1
        , s_0() -> 1
        , s_0() -> 2
        , s_1() -> 1
        , cons_0(2) -> 1
        , cons_0(2) -> 2
        , cons_1(2) -> 1
        , from_0(2) -> 1
        , add_0(2, 2) -> 1
        , len_0(2) -> 1}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(1))
Input	Transformed CSR 04 Ex2 Luc03b L

stdout:

YES(?,O(1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex2 Luc03b L

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  fst(0(), Z) -> nil()
     , fst(s(), cons(Y)) -> cons(Y)
     , from(X) -> cons(X)
     , add(0(), X) -> X
     , add(s(), Y) -> s()
     , len(nil()) -> 0()
     , len(cons(X)) -> s()}

Proof Output:
  'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:

  Details:
  --------
    'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
     'Bounds with minimal-enrichment and initial automaton 'match''
     --------------------------------------------------------------
     Answer:           YES(?,O(n^1))
     Input Problem:    runtime-complexity with respect to
       Rules:
         {  fst(0(), Z) -> nil()
          , fst(s(), cons(Y)) -> cons(Y)
          , from(X) -> cons(X)
          , add(0(), X) -> X
          , add(s(), Y) -> s()
          , len(nil()) -> 0()
          , len(cons(X)) -> s()}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  fst_0(2, 2) -> 1
        , 0_0() -> 1
        , 0_0() -> 2
        , 0_1() -> 1
        , nil_0() -> 1
        , nil_0() -> 2
        , nil_1() -> 1
        , s_0() -> 1
        , s_0() -> 2
        , s_1() -> 1
        , cons_0(2) -> 1
        , cons_0(2) -> 2
        , cons_1(2) -> 1
        , from_0(2) -> 1
        , add_0(2, 2) -> 1
        , len_0(2) -> 1}